We see increased uncertainty in \(\cos \theta \)  with respect to those obtained from the Default model from [1]}. While the tilt distribution of the Default model is astrophysically-motivated, it is incapable of capturing any possible substructure that may be present at locations other than \(\cos \theta = 1\) , as it is modeled by a monotonic function. Given the additional flexibility of the spline model, we notice a trend in the average line of the \(\cos (\theta )\)  distribution toward increased support for \(-0.25 < \cos \theta < 0.5\) . This trend is of low significance given the uncertainties surrounding it in the inferred \(\cos \theta \)  parameter space, but may indicate a nontrivial contribution from BBHs with in-plane spins to the astrophysical population. This trend is consistent with what is found in [2]}, in which the authors add several more statistically-motivated parametric models to the \(\cos \theta \)  distribution in order to increase model flexibility. Our result that \({38.6\%}^{+17.3\%}_{-15.6\%}\)  of BHs exhibit negative spin tilts is broadly consistent with previous studies that indicate the need for negative alignment in the astrophysical population. The presence of support for \(\cos \theta < 0\)  in the population was reported in [3]} and confirmed in subsequent studies (e.g. [4]}, [1]}).
